I live in Houston, as well. Six month ago I found a couple of old metal cans of powder in the garage. Both where bought back in the mid-80s and forgot about in the mid-90s. So, I had some powder that was already ten years old and left in the garage for another ten. Two different brands; one was bad, the other good.
So, even with excessive heat and cold, it would take several years for powder to degrade. The biggest problem is humidity. Powder is sealed in a container, so no problem there. Maybe, use a ammo can to keep your primers in.
If in doubt, keep it inside. A nice dark closet do…